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Anybody kindly help me to find how to calculate pressure in bar from flow rate. I have a pipe and from that I am transferring water at a constant flow rate of 5ml/min. At this flow rate, with a 0.5 cm diameter pipe, what will be the pressure generated by water?

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Potential duplicate with physics.stackexchange.com/q/126583 –  Whelp Jul 23 at 13:20

1 Answer 1

If the flow is laminar, i.e. not turbulent, then the relationship between flow rate and pressure is given by the Hagen–Poiseuille equation:

$$\text{Flow rate} = \frac{\pi r^4 (P - P_0)}{8 \eta l}$$

where $r$ is the radius of the pipe or tube, $P_0$ is the fluid pressure at one end of the pipe, $P$ is the fluid pressure at the other end of the pipe, $\eta$ is the fluid's viscosity, and $l$ is the length of the pipe or tube.

For turbulent flow there is no simple analytic treatment, but there is an empirical equation called the Darcy–Weisbach equation:

$$ P - P_0 = f_D \frac{l}{2r} \frac{\rho V^2}{2} $$

where $V$ is the flow velocity and $f_D$ is an empirically measured constant called the Darcy friction factor.

There is an online calculator for the Darcy-Weisback equation here.

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I think this answer should at least mention the famous Moody diagram ( en.wikipedia.org/wiki/Moody_diagram ). Which is basically a graphical representation of $f_D$. –  Bernhard Jul 23 at 11:40

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